i gave up crate training princess after a very short time, as i could hear her crying as i left the house & returned. (tho i know many are successful), so i started partitioning her off in the kitchen. at the other end of the kitchen is the carpeted hallway. even though it was blocked off she could still get to some of the carpet-and she proved it! what i ended up doing is actually nailing down a throw rug to hide the edge & she finally gave up and is doing better now...i think you said you have an ex-pen or something, is there anyway you could get a cheap rug or even a sheet & secure it underneath so she'll leave the carpet alone?
also then maybe your other dog could be with her...it probably bothers her even more to be away from all of you, so maybe if they could be together she wouldn't feel so lonely. just a thought.
hope it works out & you find a solution.